>In other words, must it be translated "the only begotten's name" or >can it be understood as "the name, (comma) the only begotten"?

There are 28 NT occurrences of "name" followed immediately by a genitive
noun: e.g., "in the name of the Lord" is pretty frequent. There are
patterns of genitive use which can help in cases like this (though one
must never use this kind of process mechanically!). Possibly one can
decide the issue by asking whether the genitive noun is a proper name,
then it might be seen as appositional: "At the name of Jesus" might mean
"at the name, 'Jesus'" (Phil. 2:10 and several places in Acts). But if
the genitive is a title or other kind of attribute, then it is more
likely to be possession "the name of the Lord" (Rom. 10:13) does not
really mean: "the name,'Lord'" (though this might be possible in other
contexts). In John 3:18 the genitive phrase is a title and fits your
first translation as possession best.

Prof. Conrad's mention of Simon Magus in connection with the power of
the divine name also brought to mind the would-be exorcists in Acts
19:13. In the OT the "name" of God sometimes represents God himself,
i.e., where God's name is, there he is (e.g., Deut. 12:5). I'm sure a
study of "name" (Heb. SHEM; rhymes with "name") in the OT would be
profitable. One interesting passage whose translation some might contest
is James 2:7 "Are not these the very ones who blaspheme the excellent
name invoked over you (in baptism)?" This is seen as a reference to the
trinitarian name of Matt. 28.